White dwarf structure in $f(R,T,L_m)$ gravity: beyond the Chandrasekhar mass limit

In this work, we investigate the relativistic structure of white dwarfs (WDs) within the framework of modified gravity theory $f(R,T,L_m)=R+\alpha T{L}_m$, which introduces a non-minimal coupling between matter and curvature. Using a realistic equation of state (EoS) that includes contributions from a relativistic degenerate electron gas and ionic lattice effects, we solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations for two standard choices of the matter Lagrangian density: $L_m=p$ and $L_m=-\rho$. We show that the extra $\alpha T{L}_m$ term significantly alters the mass-radius relation of WDs, especially at high central densities $({\rho }_c\gtrsim {10}^8-{10}^9\mathrm{g}\mathrm{/}\mathrm{c}{\mathrm{m}}^3)$, allowing for stable super-Chandrasekhar configurations. In particular, depending on the sign and magnitude of the parameter $\alpha$, the maximum mass can increase or decrease, and in some regimes, the usual critical point indicating the transition from stability to instability disappears. Our findings suggest that $f(R,T,L_m)$ gravity provides a viable framework to explain the existence of massive WDs beyond the classical Chandrasekhar limit. Using Bayesian inference with WD observational data, we further constrain the coupling parameter $\alpha$ for the two choices of the Lagrangian density $L_m$.